on donne a²+b²+c²=1
(a²)²+(ab+c)²+(ac-b)²
= (aa)²+((ab)²+2abc+c²)+((ac)²-2acb+b²
=(aa)²+(ab)²+2abc+c²+(ac)²-2acb+b²
=(aa)²+(ab)²+(ac)²+c²+b²+2abc-2acb
=(aa)²+(ab)²+(ac)²+c²+b²
=a²(a²+b²+c²)+c²+b² ( en remplace a²+b²+c² par 1 )
=a²+b²+c²
=1
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on donne a²+b²+c²=1
(a²)²+(ab+c)²+(ac-b)²
= (aa)²+((ab)²+2abc+c²)+((ac)²-2acb+b²
=(aa)²+(ab)²+2abc+c²+(ac)²-2acb+b²
=(aa)²+(ab)²+(ac)²+c²+b²+2abc-2acb
=(aa)²+(ab)²+(ac)²+c²+b²
=a²(a²+b²+c²)+c²+b² ( en remplace a²+b²+c² par 1 )
=a²+b²+c²
=1